A probabilistic position value

Abstract

In this article, we generalize the position value, defined by Meessen (Master's thesis, 1988) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations (Gómez et al. in European Journal of Operational Research 190:539-556, 2008). We provide two characterizations of this new allocation rule. Following in Slikker's (International Journal of Game Theory 33:505-514, 2005a) footsteps, we characterize the probabilistic position value using probabilistic versions of component efficiency and balanced link contributions. Then we generalize the notion of link potential, defined by Slikker (International Game Theory Review 7:473-489, 2005b) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations, and use it to characterize our allocation rule.